What are the solutions to the equation x^2-sqrt(2)x-1=0 ?

The solutions to the equation x^2-sqrt(2)x-1=0 are x=(sqrt(2)+sqrt(6))/2 ,x=(sqrt(2)-sqrt(6))/2

Find the zeros of x^2-sqrt(2)x-1=0

The zeros of x^2-sqrt(2)x-1=0 are x=(sqrt(2)+sqrt(6))/2 ,x=(sqrt(2)-sqrt(6))/2

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x^{2} - 2 x - 1 = 0

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}

Decimal Notation

x = 1.93185 \dots, x = - 0.51763 \dots

Solution steps

x^{2} - 2 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 1 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 1) = 6

x_{1, 2} = \frac{- ( - 2 ) \pm 6}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 6}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 6}{2 \cdot 1}

x = \frac{- ( - 2 ) + 6}{2 \cdot 1} : \frac{2 + 6}{2}

x = \frac{- ( - 2 ) - 6}{2 \cdot 1} : \frac{2 - 6}{2}

The solutions to the quadratic equation are:

x = \frac{2 + 6}{2}, x = \frac{2 - 6}{2}

2 x = 24

2 x = 12

7 x^{2} - 33 x - 10 = 0

- 10 n^{2} - 25 n + 20

\frac{32 !}{( 32 - 4 ) ! 4 !}

What are the solutions to the equation x^2-sqrt(2)x-1=0 ?
The solutions to the equation x^2-sqrt(2)x-1=0 are x=(sqrt(2)+sqrt(6))/2 ,x=(sqrt(2)-sqrt(6))/2
Find the zeros of x^2-sqrt(2)x-1=0
The zeros of x^2-sqrt(2)x-1=0 are x=(sqrt(2)+sqrt(6))/2 ,x=(sqrt(2)-sqrt(6))/2